Question: Factor completely. $81p ^8-100 =$
Solution: $81 p ^8 -100 = ({9 p ^4})^2-({10 })^2$ Using the difference of squares pattern: $({9 p ^4})^2 - ({10 })^2 =({9 p ^4}+{10 })({9 p ^4}-{10 })$ In conclusion, $81 p ^8-100 =(9 p ^4+10 )(9 p ^4-10 )$ Remember that you can always check your factorization by expanding it.